Deep learning based on mixed-variable physics informed neural network for solving fluid dynamics without simulation data

Deep learning method has attracted tremendous attention to handle fluid dynamics in recent years. However, the deep learning method requires much data to guarantee the generalization ability and the data of fluid dynamics are deficient. Recently, physics informed neural network (PINN) is popular to solve the fluid flow problems, which basic concept is to embed the governing equation and continuity equation into loss function, with the requirement of less dataset for obtaining a reliable neural network. In this paper, the mixed-variable PINN method, which convert the governing equation into continuum and constitutive formulations, is proposed to solve the fluid dynamics (flow past cylinder) without any labeled data. The initial/boundary conditions with penalty factors are also embedded into the loss function to become a well-imposed problem. The results show that mixed-variable PINN has better predictive ability to construct the flow field than traditional PINN scheme. Furthermore, the transfer learning method is adopted to is solve the fluid solutions with different Reynold numbers with less computational cost. The results also demonstrate that the transfer learning method can well simulate the different Reynolds number in a short time.